To make the buttermilk brine, in a large bowl, whisk together the buttermilk and salt. In a mortar, crush together the oregano, thyme, rosemary, and sage with a pestle (or pulse in a spice grinder) until finely ground. Whisk the ground herbs, garlic, and cayenne pepper into the buttermilk mixture. Cut each chicken breast half crosswise to make 4 breast portions, for a total of 10 chicken pieces. Add to the buttermilk brine, making sure that the chicken is submerged. (If it isn't, transfer everything to a smaller bowl.) Cover and refrigerate for at least 4 hours and up to 6 hours.

Pour oil into a large, heavy saucepan to a depth of at least 3 inches (7.5 cm) and heat to 350° F (180°) on a deep-frying thermometer. (If you don't have a thermometer, your best test is to dip the edge of a tortilla or bread slice into the oil; it should sizzle immediately and vigorously.) Set a large wire rack on a rimmed baking sheet and place near the stove. Have ready a second rimmed baking sheet. In a large bowl, whisk together the flour, baking powder, and black pepper. Remove half of the chicken from the buttermilk brine, letting the excess brine drip back into the bowl. Add the chicken to the flour mixture and toss to coat evenly, then transfer to the second baking sheet.

When the oil is ready, working in batches to avoid crowding, carefully slip the chicken pieces into the hot oil. The temperature will drop, but adjust the heat to keep the oil bubbling steadily at about 325° F (165°). Deep-fry the chicken pieces, turning them occasionally with tongs, until they are golden brown and show no sign of pink when pierced at the thickest part, about 12 minutes. Using a wire skimmer, transfer the chicken to the rack to drain. Repeat with the remaining chicken. Serve warm.